- Ground truth 1
- Ground truth 2
- Ground truth 3
Ground truth 1
There is - no interaction and - no ceiling effect in the moderator, - no floor effect in the outcome. - two main effects on the outcome, one positive, one negative.
knitr::opts_chunk$set(error = TRUE)set.seed(1710)
library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(ggplot2)
library(brms)## Loading required package: Rcpp## Loading 'brms' package (version 2.1.0). Useful instructions
## can be found by typing help('brms'). A more detailed introduction
## to the package is available through vignette('brms_overview').
## Run theme_set(theme_default()) to use the default bayesplot theme.library(broom)
multiplot <- function(x) { x %>% purrr::map(function(.) { tidy(., conf.int = TRUE, par_type = "non-varying") }) %>%
bind_rows(.id = "model") %>%
ggplot(aes(term, estimate, ymin = lower, ymax = upper, color = model)) +
geom_pointrange(position = position_dodge(width = 0.3)) + coord_flip()
}
likert <- function(x) { round(scales::squish(x, c(1,6))) }
dist1 = data_frame(
pred = rnorm(1000),
pred_m = likert(pred + 3),
mod = rnorm(1000),
mod_m = likert(mod + 3),
outcome = pred + -1 * mod + rnorm(1000, sd = 3),
outcome_m = likert(outcome + 3)
)
ggplot(dist1, aes(pred, outcome)) + facet_wrap(~ mod_m) +
geom_jitter() +
geom_smooth(method = 'lm', se = F)
ggplot(dist1, aes(pred_m, outcome_m)) + facet_wrap(~ mod_m) +
geom_jitter() +
geom_smooth(method = 'lm', se = F)
summary(g1m1r <- brm(bf(outcome ~ pred + mod), data = dist1, cores = 3, chains = 3))## Compiling the C++ model## Start sampling## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: outcome ~ pred + mod
## Data: dist1 (Number of observations: 1000)
## Samples: 3 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup samples = 3000
## ICs: LOO = NA; WAIC = NA; R2 = NA
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
## Intercept -0.07 0.09 -0.26 0.11 3000 1.00
## pred 1.03 0.09 0.85 1.22 2978 1.00
## mod -1.12 0.10 -1.30 -0.92 3000 1.00
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
## sigma 2.86 0.06 2.74 2.99 3000 1.00
##
## Samples were drawn using sampling(NUTS). For each parameter, Eff.Sample
## is a crude measure of effective sample size, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).summary(g1m2r <- brm(bf(outcome ~ pred * mod), data = dist1, cores = 3, chains = 3))## Compiling the C++ model
## Start sampling## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: outcome ~ pred * mod
## Data: dist1 (Number of observations: 1000)
## Samples: 3 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup samples = 3000
## ICs: LOO = NA; WAIC = NA; R2 = NA
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
## Intercept -0.07 0.09 -0.25 0.11 3000 1.00
## pred 1.03 0.09 0.84 1.21 3000 1.00
## mod -1.12 0.10 -1.31 -0.93 3000 1.00
## pred:mod 0.08 0.10 -0.11 0.27 3000 1.00
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
## sigma 2.86 0.06 2.74 2.99 3000 1.00
##
## Samples were drawn using sampling(NUTS). For each parameter, Eff.Sample
## is a crude measure of effective sample size, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).LOO(g1m1r, g1m2r)## LOOIC SE
## g1m1r 4945.01 42.05
## g1m2r 4946.13 41.89
## g1m1r - g1m2r -1.12 1.65list(g1m1r, g1m2r) %>% multiplot
summary(g1m1 <- brm(bf(outcome_m ~ pred_m + mod_m), data = dist1, cores = 3, chains = 3))## Compiling the C++ model
## Start sampling## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: outcome_m ~ pred_m + mod_m
## Data: dist1 (Number of observations: 1000)
## Samples: 3 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup samples = 3000
## ICs: LOO = NA; WAIC = NA; R2 = NA
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
## Intercept 3.39 0.26 2.90 3.89 3000 1.00
## pred_m 0.52 0.06 0.40 0.63 3000 1.00
## mod_m -0.58 0.06 -0.69 -0.46 3000 1.00
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
## sigma 1.84 0.04 1.76 1.92 3000 1.00
##
## Samples were drawn using sampling(NUTS). For each parameter, Eff.Sample
## is a crude measure of effective sample size, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).summary(g1m2 <- brm(bf(outcome_m ~ pred_m * mod_m), data = dist1, cores = 3, chains = 3))## Compiling the C++ model
## Start sampling## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: outcome_m ~ pred_m * mod_m
## Data: dist1 (Number of observations: 1000)
## Samples: 3 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup samples = 3000
## ICs: LOO = NA; WAIC = NA; R2 = NA
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
## Intercept 3.27 0.61 2.12 4.47 921 1.00
## pred_m 0.56 0.19 0.16 0.92 915 1.00
## mod_m -0.54 0.19 -0.92 -0.17 912 1.00
## pred_m:mod_m -0.01 0.06 -0.12 0.11 893 1.00
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
## sigma 1.84 0.04 1.76 1.92 2125 1.00
##
## Samples were drawn using sampling(NUTS). For each parameter, Eff.Sample
## is a crude measure of effective sample size, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).LOO(g1m1, g1m2)## LOOIC SE
## g1m1 4054.21 29.98
## g1m2 4055.86 30.05
## g1m1 - g1m2 -1.65 0.41list(g1m1, g1m2) %>% multiplot
summary(g1mc1 <- brm(bf(outcome_m ~ pred_m + mod_m), data = dist1, cores = 3, chains = 3, family = cumulative(threshold = "equidistant")))## Compiling the C++ model
## Start sampling## Family: cumulative
## Links: mu = logit; disc = identity
## Formula: outcome_m ~ pred_m + mod_m
## Data: dist1 (Number of observations: 1000)
## Samples: 3 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup samples = 3000
## ICs: LOO = NA; WAIC = NA; R2 = NA
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
## Intercept[1] -0.93 0.26 -1.45 -0.42 2674 1.00
## Intercept[2] -0.39 0.26 -0.90 0.12 2701 1.00
## Intercept[3] 0.15 0.26 -0.36 0.64 2724 1.00
## Intercept[4] 0.69 0.26 0.18 1.19 2741 1.00
## Intercept[5] 1.23 0.26 0.72 1.73 2741 1.00
## pred_m 0.54 0.06 0.43 0.66 2334 1.00
## mod_m -0.58 0.06 -0.71 -0.47 2733 1.00
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
## delta 0.54 0.02 0.50 0.59 2375 1.00
##
## Samples were drawn using sampling(NUTS). For each parameter, Eff.Sample
## is a crude measure of effective sample size, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).summary(g1mc2 <- brm(bf(outcome_m ~ pred_m * mod_m), data = dist1, cores = 3, chains = 3, family = cumulative( threshold = "equidistant")))## Compiling the C++ model
## Start sampling## Family: cumulative
## Links: mu = logit; disc = identity
## Formula: outcome_m ~ pred_m * mod_m
## Data: dist1 (Number of observations: 1000)
## Samples: 3 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup samples = 3000
## ICs: LOO = NA; WAIC = NA; R2 = NA
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
## Intercept[1] -0.83 0.63 -2.04 0.41 1238 1.00
## Intercept[2] -0.29 0.63 -1.50 0.93 1239 1.00
## Intercept[3] 0.25 0.63 -0.96 1.47 1241 1.00
## Intercept[4] 0.79 0.63 -0.44 2.01 1243 1.00
## Intercept[5] 1.33 0.63 0.11 2.56 1247 1.00
## pred_m 0.57 0.20 0.20 0.96 1212 1.00
## mod_m -0.56 0.20 -0.94 -0.16 1193 1.00
## pred_m:mod_m -0.01 0.06 -0.13 0.11 1144 1.00
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
## delta 0.54 0.02 0.50 0.58 1757 1.00
##
## Samples were drawn using sampling(NUTS). For each parameter, Eff.Sample
## is a crude measure of effective sample size, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).LOO(g1mc1, g1mc2)## LOOIC SE
## g1mc1 3183.64 42.42
## g1mc2 3185.52 42.50
## g1mc1 - g1mc2 -1.87 0.34list(g1mc1, g1mc2) %>% multiplot
list(g1m1, g1m2, g1mc1, g1mc2) %>% multiplot
Ground truth 2
There is no interaction, but a floor effect in the outcome
dist1 = dist1 %>% mutate(
outcome_m = likert(outcome - 1)
)
table(dist1$outcome_m)##
## 1 2 3 4 5 6
## 774 93 64 29 24 16ggplot(dist1, aes(pred, outcome)) + facet_wrap(~ mod_m) +
geom_jitter() +
geom_smooth(method = 'lm', se = F)
ggplot(dist1, aes(pred_m, outcome_m)) + facet_wrap(~ mod_m) +
geom_jitter() +
geom_smooth(method = 'lm', se = F)
summary(g1m1r <- brm(bf(outcome ~ pred + mod), data = dist1, cores = 3, chains = 3))## Compiling the C++ model## Start sampling## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: outcome ~ pred + mod
## Data: dist1 (Number of observations: 1000)
## Samples: 3 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup samples = 3000
## ICs: LOO = NA; WAIC = NA; R2 = NA
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
## Intercept -0.07 0.09 -0.25 0.11 3000 1.00
## pred 1.03 0.09 0.86 1.21 3000 1.00
## mod -1.11 0.10 -1.30 -0.93 3000 1.00
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
## sigma 2.86 0.06 2.74 3.00 3000 1.00
##
## Samples were drawn using sampling(NUTS). For each parameter, Eff.Sample
## is a crude measure of effective sample size, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).summary(g1m2r <- brm(bf(outcome ~ pred * mod), data = dist1, cores = 3, chains = 3))## Compiling the C++ model
## Start sampling## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: outcome ~ pred * mod
## Data: dist1 (Number of observations: 1000)
## Samples: 3 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup samples = 3000
## ICs: LOO = NA; WAIC = NA; R2 = NA
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
## Intercept -0.06 0.09 -0.25 0.12 3000 1.00
## pred 1.03 0.09 0.85 1.21 3000 1.00
## mod -1.12 0.10 -1.30 -0.93 3000 1.00
## pred:mod 0.08 0.10 -0.11 0.27 3000 1.00
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
## sigma 2.87 0.06 2.74 3.00 3000 1.00
##
## Samples were drawn using sampling(NUTS). For each parameter, Eff.Sample
## is a crude measure of effective sample size, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).LOO(g1m1r, g1m2r)## LOOIC SE
## g1m1r 4944.76 42.03
## g1m2r 4946.13 41.83
## g1m1r - g1m2r -1.37 1.62list(g1m1r, g1m2r) %>% multiplot
summary(g1m1 <- brm(bf(outcome_m ~ pred_m + mod_m), data = dist1, cores = 3, chains = 3))## Compiling the C++ model
## Start sampling## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: outcome_m ~ pred_m + mod_m
## Data: dist1 (Number of observations: 1000)
## Samples: 3 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup samples = 3000
## ICs: LOO = NA; WAIC = NA; R2 = NA
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
## Intercept 1.65 0.15 1.37 1.94 3000 1.00
## pred_m 0.21 0.03 0.14 0.27 3000 1.00
## mod_m -0.26 0.03 -0.33 -0.20 3000 1.00
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
## sigma 1.03 0.02 0.98 1.07 3000 1.00
##
## Samples were drawn using sampling(NUTS). For each parameter, Eff.Sample
## is a crude measure of effective sample size, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).summary(g1m2 <- brm(bf(outcome_m ~ pred_m * mod_m), data = dist1, cores = 3, chains = 3))## Compiling the C++ model
## Start sampling## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: outcome_m ~ pred_m * mod_m
## Data: dist1 (Number of observations: 1000)
## Samples: 3 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup samples = 3000
## ICs: LOO = NA; WAIC = NA; R2 = NA
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
## Intercept 0.93 0.34 0.25 1.59 1297 1.00
## pred_m 0.44 0.11 0.24 0.65 1275 1.00
## mod_m -0.03 0.11 -0.23 0.18 1234 1.00
## pred_m:mod_m -0.08 0.03 -0.14 -0.01 1226 1.00
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
## sigma 1.02 0.02 0.98 1.07 2170 1.00
##
## Samples were drawn using sampling(NUTS). For each parameter, Eff.Sample
## is a crude measure of effective sample size, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).LOO(g1m1, g1m2)## LOOIC SE
## g1m1 2895.90 85.94
## g1m2 2892.93 87.03
## g1m1 - g1m2 2.98 5.84list(g1m1, g1m2) %>% multiplot
summary(g1mc1 <- brm(bf(outcome_m ~ pred_m + mod_m), data = dist1, cores = 3, chains = 3, family = cumulative(threshold = "equidistant")))## Compiling the C++ model
## Start sampling## Family: cumulative
## Links: mu = logit; disc = identity
## Formula: outcome_m ~ pred_m + mod_m
## Data: dist1 (Number of observations: 1000)
## Samples: 3 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup samples = 3000
## ICs: LOO = NA; WAIC = NA; R2 = NA
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
## Intercept[1] 0.95 0.35 0.27 1.62 3000 1.00
## Intercept[2] 1.69 0.35 1.01 2.37 3000 1.00
## Intercept[3] 2.43 0.36 1.73 3.13 3000 1.00
## Intercept[4] 3.17 0.37 2.43 3.89 3000 1.00
## Intercept[5] 3.90 0.39 3.14 4.68 3000 1.00
## pred_m 0.52 0.08 0.36 0.68 2877 1.00
## mod_m -0.67 0.09 -0.84 -0.51 3000 1.00
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
## delta 0.74 0.05 0.65 0.83 3000 1.00
##
## Samples were drawn using sampling(NUTS). For each parameter, Eff.Sample
## is a crude measure of effective sample size, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).summary(g1mc2 <- brm(bf(outcome_m ~ pred_m * mod_m), data = dist1, cores = 3, chains = 3, family = cumulative( threshold = "equidistant")))## Compiling the C++ model
## Start sampling## Family: cumulative
## Links: mu = logit; disc = identity
## Formula: outcome_m ~ pred_m * mod_m
## Data: dist1 (Number of observations: 1000)
## Samples: 3 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup samples = 3000
## ICs: LOO = NA; WAIC = NA; R2 = NA
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
## Intercept[1] 1.60 0.87 -0.10 3.28 1150 1.00
## Intercept[2] 2.35 0.87 0.65 4.05 1152 1.00
## Intercept[3] 3.09 0.87 1.40 4.81 1158 1.00
## Intercept[4] 3.83 0.88 2.13 5.55 1168 1.00
## Intercept[5] 4.57 0.89 2.85 6.28 1180 1.00
## pred_m 0.72 0.25 0.22 1.22 1118 1.00
## mod_m -0.44 0.30 -1.03 0.15 1132 1.00
## pred_m:mod_m -0.07 0.09 -0.24 0.10 1117 1.00
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
## delta 0.74 0.05 0.65 0.84 1981 1.00
##
## Samples were drawn using sampling(NUTS). For each parameter, Eff.Sample
## is a crude measure of effective sample size, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).LOO(g1mc1, g1mc2)## LOOIC SE
## g1mc1 1607.88 70.18
## g1mc2 1609.27 70.48
## g1mc1 - g1mc2 -1.39 1.76list(g1mc1, g1mc2) %>% multiplot
list(g1m1, g1m2, g1mc1, g1mc2) %>% multiplot
Ground truth 3
There is an interaction, and a floor effect in the outcome.
dist1 = dist1 %>% mutate(
outcome = pred + -1 * mod + 0.5*pred*mod + rnorm(1000, sd = 3),
outcome_m = likert(outcome - 1)
)
table(dist1$outcome_m)##
## 1 2 3 4 5 6
## 784 76 55 36 24 25ggplot(dist1, aes(pred, outcome)) + facet_wrap(~ mod_m) +
geom_jitter() +
geom_smooth(method = 'lm', se = F)
ggplot(dist1, aes(pred_m, outcome_m)) + facet_wrap(~ mod_m) +
geom_jitter() +
geom_smooth(method = 'lm', se = F)
summary(g1m1r <- brm(bf(outcome ~ pred + mod), data = dist1, cores = 3, chains = 3))## Compiling the C++ model## Start sampling## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: outcome ~ pred + mod
## Data: dist1 (Number of observations: 1000)
## Samples: 3 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup samples = 3000
## ICs: LOO = NA; WAIC = NA; R2 = NA
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
## Intercept -0.09 0.10 -0.28 0.11 3000 1.00
## pred 1.12 0.10 0.93 1.31 3000 1.00
## mod -0.87 0.10 -1.06 -0.67 3000 1.00
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
## sigma 3.06 0.07 2.93 3.19 3000 1.00
##
## Samples were drawn using sampling(NUTS). For each parameter, Eff.Sample
## is a crude measure of effective sample size, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).summary(g1m2r <- brm(bf(outcome ~ pred * mod), data = dist1, cores = 3, chains = 3))## Compiling the C++ model
## Start sampling## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: outcome ~ pred * mod
## Data: dist1 (Number of observations: 1000)
## Samples: 3 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup samples = 3000
## ICs: LOO = NA; WAIC = NA; R2 = NA
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
## Intercept -0.06 0.10 -0.24 0.13 3000 1.00
## pred 1.09 0.10 0.89 1.29 3000 1.00
## mod -0.92 0.11 -1.12 -0.71 3000 1.00
## pred:mod 0.60 0.10 0.41 0.79 3000 1.00
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
## sigma 3.00 0.07 2.88 3.14 3000 1.00
##
## Samples were drawn using sampling(NUTS). For each parameter, Eff.Sample
## is a crude measure of effective sample size, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).LOO(g1m1r, g1m2r)## LOOIC SE
## g1m1r 5073.82 44.74
## g1m2r 5041.13 43.65
## g1m1r - g1m2r 32.69 13.89list(g1m1r, g1m2r) %>% multiplot
summary(g1m1 <- brm(bf(outcome_m ~ pred_m + mod_m), data = dist1, cores = 3, chains = 3))## Compiling the C++ model
## Start sampling## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: outcome_m ~ pred_m + mod_m
## Data: dist1 (Number of observations: 1000)
## Samples: 3 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup samples = 3000
## ICs: LOO = NA; WAIC = NA; R2 = NA
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
## Intercept 1.40 0.16 1.10 1.72 3000 1.00
## pred_m 0.22 0.04 0.15 0.29 3000 1.00
## mod_m -0.18 0.04 -0.26 -0.11 3000 1.00
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
## sigma 1.14 0.03 1.09 1.19 3000 1.00
##
## Samples were drawn using sampling(NUTS). For each parameter, Eff.Sample
## is a crude measure of effective sample size, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).summary(g1m2 <- brm(bf(outcome_m ~ pred_m * mod_m), data = dist1, cores = 3, chains = 3))## Compiling the C++ model
## Start sampling## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: outcome_m ~ pred_m * mod_m
## Data: dist1 (Number of observations: 1000)
## Samples: 3 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup samples = 3000
## ICs: LOO = NA; WAIC = NA; R2 = NA
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
## Intercept 1.59 0.38 0.84 2.35 886 1.00
## pred_m 0.16 0.12 -0.07 0.39 919 1.00
## mod_m -0.25 0.12 -0.48 -0.01 888 1.00
## pred_m:mod_m 0.02 0.04 -0.05 0.09 923 1.00
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
## sigma 1.14 0.03 1.09 1.18 1876 1.00
##
## Samples were drawn using sampling(NUTS). For each parameter, Eff.Sample
## is a crude measure of effective sample size, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).LOO(g1m1, g1m2)## LOOIC SE
## g1m1 3095.82 84.03
## g1m2 3098.08 83.98
## g1m1 - g1m2 -2.26 1.17list(g1m1, g1m2) %>% multiplot
summary(g1mc1 <- brm(bf(outcome_m ~ pred_m + mod_m), data = dist1, cores = 3, chains = 3, family = cumulative(threshold = "equidistant")))## Compiling the C++ model
## Start sampling## Family: cumulative
## Links: mu = logit; disc = identity
## Formula: outcome_m ~ pred_m + mod_m
## Data: dist1 (Number of observations: 1000)
## Samples: 3 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup samples = 3000
## ICs: LOO = NA; WAIC = NA; R2 = NA
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
## Intercept[1] 1.83 0.36 1.17 2.57 3000 1.00
## Intercept[2] 2.43 0.36 1.76 3.15 3000 1.00
## Intercept[3] 3.02 0.37 2.33 3.76 3000 1.00
## Intercept[4] 3.61 0.38 2.91 4.38 3000 1.00
## Intercept[5] 4.21 0.39 3.46 5.00 3000 1.00
## pred_m 0.53 0.08 0.37 0.68 2877 1.00
## mod_m -0.39 0.08 -0.55 -0.22 3000 1.00
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
## delta 0.59 0.04 0.52 0.67 3000 1.00
##
## Samples were drawn using sampling(NUTS). For each parameter, Eff.Sample
## is a crude measure of effective sample size, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).summary(g1mc2 <- brm(bf(outcome_m ~ pred_m * mod_m), data = dist1, cores = 3, chains = 3, family = cumulative( threshold = "equidistant")))## Compiling the C++ model
## Start sampling## Family: cumulative
## Links: mu = logit; disc = identity
## Formula: outcome_m ~ pred_m * mod_m
## Data: dist1 (Number of observations: 1000)
## Samples: 3 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup samples = 3000
## ICs: LOO = NA; WAIC = NA; R2 = NA
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
## Intercept[1] 0.02 0.86 -1.60 1.67 1150 1.00
## Intercept[2] 0.62 0.86 -1.01 2.26 1149 1.00
## Intercept[3] 1.21 0.86 -0.42 2.87 1150 1.00
## Intercept[4] 1.80 0.86 0.16 3.47 1153 1.00
## Intercept[5] 2.40 0.87 0.74 4.09 1159 1.00
## pred_m -0.01 0.25 -0.49 0.47 1134 1.00
## mod_m -1.03 0.30 -1.60 -0.46 1138 1.00
## pred_m:mod_m 0.19 0.08 0.03 0.35 1107 1.00
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
## delta 0.59 0.04 0.52 0.67 2210 1.00
##
## Samples were drawn using sampling(NUTS). For each parameter, Eff.Sample
## is a crude measure of effective sample size, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).LOO(g1mc1, g1mc2)## LOOIC SE
## g1mc1 1637.05 72.69
## g1mc2 1633.81 72.52
## g1mc1 - g1mc2 3.23 4.49list(g1mc1, g1mc2) %>% multiplot
list(g1m1, g1m2, g1mc1, g1mc2) %>% multiplot